Find a monic irreducible polynomial $f(x) = (x - x_1) ... (x - x_n)$, $|x_1| > 1$ and $x_1$ is real, |x_2| < 1 and $x_2$ is real, $|x_j| = 1$ for all $j > 2$. And First, prove $n > 3$ and it must be even. I can prove $n>3$ and $n$ is even using the resolvent of quartic equation with leading coefficient 1. It is easy to know that there is an $m$ making $(x-x_3)...(x-x_n)$ is equivalent to $\Phi_m$.
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This question absolutely needs to be linked to here. I still suspect that we have a close enough duplicate somewhere. I just haven't found the right keywords. – Jyrki Lahtonen May 24 '24 at 07:08